Very clever complex inequality.

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mathwizarddud
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Prove that for every complex number z it happens that:

[tex]|z+10|+|z+11|+|z+19| \le |z+8|+|z+12|+|z+20|[/tex]
 

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let z = a+ bi and physically evaluate the modulus.

Is this some homework question? I am not sure why this is in the analysis section.
 

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